The LSAT a test taken for law school admission has a mean sc

The LSAT (a test taken for law school admission) has a mean score of 151 with a standard deviation of 9 and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of 9 students at a time. A larger organization teaches classes of 25 students at a time. Both organizations publish the mean scores of all their classes.

a) what would you expect the distribution of mean class scores to be for each organization?

b) if either organization has a graduating class with a mean score og 160, they\'ll take out a full-page ad in the local school paper to advertise. which organization is more likely to have that success? explain.

c) both organizations advertise that if any class has an average score below 145, they\'ll pay for everyone to retake the LSAT. which organization is at greater risk to have to pay?

Solution

a)

They will both be approximately normally distirbuted, by central limit theorem. However, the smaller class will have sampling distribution of means which has more variation.

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b)

It will be the small classes, becasue they have more variation, it is more likely that they can go at some distance from the mean.

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c)

It will be the small classes, becasue they have more variation, it is more likely that they can go at some distance from the mean.